(→Example) |
(→Example) |
||
| Line 5: | Line 5: | ||
== Example == | == Example == | ||
| − | '''<math>y(t) = x(t) + x(t^2)</math>'''<br> | + | '''<math>y(t) = x(t) + x(t^2)\,</math>'''<br> |
If t equals to 2, <math>y(2) = x(2) + x(4)</math>. | If t equals to 2, <math>y(2) = x(2) + x(4)</math>. | ||
Then the output depends on the present and future inputs. So the system is memoryless. | Then the output depends on the present and future inputs. So the system is memoryless. | ||
Revision as of 09:32, 13 September 2008
Memoryless System & System with Memory
- A system is memoryless if for any t0, the output y(t0) only depends on the present input, x(t0).The output doesn't depend on past or future input, x(t0 + k) for any integer k.
- A system is a system with memory if for any t0, the output y(t0) depends on not only the present input, x(t0) but also the past or future, x(t0 + k) for any integer k.
Example
$ y(t) = x(t) + x(t^2)\, $
If t equals to 2, $ y(2) = x(2) + x(4) $.
Then the output depends on the present and future inputs. So the system is memoryless.
